St. Augustine

“But by the prayers of the Holy Church, and by the salvific sacrifice, and by the alms which are given for their spirits, there is no doubt that the dead are aided, that the Lord might deal more mercifully with them than their sins would deserve. The whole Church observes this practice which was handed down by the Fathers: that it prays for those who have died in the communion of the Body and Blood of Christ, when they are commemorated in their own place in the sacrifice itself; and the sacrifice is offered also in memory of them, on their behalf. If, then, works of mercy are celebrated for the sake of those who are being remembered, who would hesitate to recommend them, on whose behalf prayers to God are not offered in vain? It is not at all to be doubted that such prayers are of profit to the dead; but for such of them as lived before their death in a way that makes it possible for these things to be useful to them after death”.

“Temporal punishments are suffered by some in this life only, by some after death, by some both here and hereafter, but all of them before that last and strictest judgment. But not all who suffer temporal punishments after death will come to eternal punishments, which are to follow after that judgment” (The City of God 21:13 [A.D. 419]).